In a skillet, heat olive oil over medium heat. Add diced potatoes and cook until golden and tender, about 15 minutes. Season with salt, black pepper, and paprika. Stir occasionally.

Make the Egg Mixture

In a bowl, whisk together the eggs, salt, and black pepper. Set aside.

Cook the Filling

In a separate skillet, melt 1 tablespoon of butter over medium heat. Add the diced onion, peppers, and ham. Sauté until the vegetables are soft and the ham is heated through, about 5-7 minutes.

Combine Filling and Eggs

Pour the egg mixture into the skillet with the ham and vegetables. Cook, stirring gently, until the eggs are just set. Add the shredded cheese and stir until melted.

Toast the Bread

In another skillet, melt the remaining tablespoon of butter. Toast the bread slices until golden brown on both sides.

Assemble the Toasted Western

Place the egg mixture on top of each slice of toasted bread. Serve with home fries on the side.